It appears simple but I am concerned about the rates that each function approaches \infty. Should I be?

Given:

 1+R=1+(T-t)L(t,T)

and

 1+R=e^{(T-t)y(t,T)

show that

 \lim_{T \rightarrow t}L(t,T) = \lim_{T \rightarrow t}y(t,T).

PROOF:

Rearrange both formulae to get:

 L(t,T)=\frac{R}{(T-t)}

and

 y(t,T)=\frac{ln(1+R)}{(T-t)}

Take the limit of each as [tex] T \rightarrow t:

 \lim_{T \rightarrow t}L(t,T)=\lim_{T \rightarrow t}\frac{R}{(T-t)} = \infty

and

 \lim_{T \rightarrow t}y(t,T)=\lim_{T \rightarrow t}\frac{ln(1+R)}{(T-t)} = \infty

As both approach \infty we can state that:

 \lim_{T \rightarrow t}L(t,T) = \lim_{T \rightarrow t}y(t,T).